Minisymposia > Multiscale numerical coupling between coarse and fine models

 

Multiscale numerical coupling between coarse and fine models

Alexei Lozinski (Université de Franche-Comté, France)
Grégory Vial (Ecole Centrale Lyon, France)

When one solves numerically a problem with localized multiscale features, one can perform first a coarse global calculation, then a finer one on a subset (zoom) of the whole domain, and eventually iterate between the two solvers until convergence. The goal of the present mini-symposium is to compare such procedures from a mathematical viewpoint.

The first question is whether one needs to iterate between the two solvers. Indeed, it can be shown in some cases, that one local correction provided by the asymptotic analysis may be enough. This is the case for the linear elasticity problem in the presence of micro-defects or for the boundary layers in a singularly perturbed diffusion reaction problem. If, however, the iterations are needed, different techniques are available to implement them using several co-existing non matching meshes: variants of Schwartz domain decomposition with complete overlap such as the method of finite element patches or the numerical zoom, the fat boundary method, Nitsche-based methods, the methods with partial overlap of two models in the interface region, etc. In any case, a posteriori error estimates are desirable in order to adjust the zoom size and position.

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